Existence of monotone solutions to some singular boundary and initial value problems

Abstract

We establish conditions sufficient to guarantee existence of nondecreasing solutions on $[0,1]$ of the differential equation $y''+f(t,y,y')=0$ subject to the boundary conditions $y(0)=0$, $y(1)=a>0$ or the initial conditions $y(0)=0$, $y'(0)=a>0$. Here $f$ is a nonnegative function which may be singular as $y\downarrow0$.